A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interiro .The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm . If length of the pencil is 10 cm, find the voluem of the wood and that of the graphite.

Explanation

Diameter of the graphite =1mm=`(1)/(10)`cm
Radius of the graphite `(R )=pir^(2)h=pixx(1)/(20)xx(1)/(20)xx(1)/(20)xx10`
`=(pi)/(40)cm^(3)`
Now diameter of the pencil `(r_(1))=7mm=(7)/(10)cm`
`therefore` Radius of the pencil`(r_(1))=(7)/(20)`cm
Volume of pencil =`pir_(1^(2))`r
`=pixx(7)/(20)xx(7)/(20)xx10=(49pi)/(40)cm^(3)`
volume of wood=volume of pencil-volume of graphite
`=((40)pi)/(40)-(pi)/(40)=(48pi)/(40)cm^(3)=(6pi)/(5)cm^(3)`